Find the value of the variable and the measure of each labeled angle (x+12) (5x-48)

Question

Find the value of the variable and the measure of each labeled angle (x+12) (5x-48)

Answer 1

x+12

5x-48

as two angles

leaves the 3rd angle as 180-(x+12)-(5x-48)= 180-6x+36= 216-6x

angle 1: x+12

angle 2 5x-48

angle 3 -6x+216

they sum to 180

x varies such that each angle >0 but <180

angle 1: x>-12, but <168

angle 2 x>48/5=9.6 but <228/5=45.6

so far: 9.6<x<45.6

angle 3 x<216/6=36, x<36 but >6

9.6<x<36

x is in the low 10 to low 30 range

angles are

1: x+12: 21.6<angle 1< 48

2: 5x-48: 48<angle 2< 132

3: -6x+216 0<angle 3<158.4

that narrows it down, a little

maybe

angle 1 is about 30

angle 2 about 90

angle 3 about 60

if you limit it to right triangles